Doc Brown's A Level Chemistry  Advanced Level Theoretical Physical Chemistry - AS A2 Level Revision Notes - Basic Thermodynamics

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Part 1 - ΔH Enthalpy Changes - The thermochemistry of enthalpies of reaction, formation, combustion and neutralisation

Part 1.1 Advanced Introduction to Enthalpy (Energy) Changes in Chemical Reactions

This page is an introduction to advanced level ideas on exothermic or endothermic energy changes in chemical reactions - referred to as 'enthalpy changes' e.g. enthalpy of reaction, enthalpy of formation, enthalpy of combustion and also bond enthalpies ('bond energies'). The concept of enthalpy level diagrams is described & introduced and enthalpy changes are clearly distinguished from activation energies. The notion of 'standard conditions' is described and why it is necessary to have data based on a standard defined temperature, pressure and concentration.

Energetics index: GCSE Notes on the basics of chemical energy changes - important to study and know before tackling any of the three Advanced Level Chemistry pages Parts 1-3 here * Part 1a-b ΔH Enthalpy Changes 1.1 Advanced Introduction to enthalpy changes - reaction, formation, combustion : 1.2a & 1.2b(i)-(iii) Thermochemistry - Hess's Law and Enthalpy Calculations - reaction, combustion, formation etc. : 1.2b(iv) Bond Enthalpy Calculations  : 1.3a-b Experimental methods for determining enthalpy changes and treatment of results : 1.4 Some enthalpy data patterns : 1.4a The combustion of linear alkanes and linear aliphatic alcohols : 1.4b Some patterns in Bond Enthalpies and Bond Length : 1.4c Enthalpies of Neutralisation : 1.4d Enthalpies of Hydrogenation of unsaturated hydrocarbons and evidence of aromatic ring structure in benzene : Extra Q page A set of practice enthalpy calculations with worked out answers ** Part 2 ΔH Enthalpies of ion hydration, solution, atomisation, lattice energy, electron affinity and the Born-Haber cycle : 2.1a-c What happens when a salt dissolves in water and why? : 2.1d-e Enthalpy cycles involving a salt dissolving : 2.2a-c The Born-Haber Cycle *** Part 3 ΔS Entropy and ΔG Free Energy Changes : 3.1a-g Introduction to Entropy : 3.2 Examples of entropy values and comments * 3.3a ΔS, Entropy and change of state : 3.3b ΔS, Entropy changes and the feasibility of a chemical change : 3.4a-d More on ΔG, Free energy changes, feasibility and applications : 3.5 Calculating Equilibrium Constants : 3.6 Kinetic stability versus thermodynamic feasibility * PLEASE note that delta H/S/G values vary slightly from source to source, so I apologise in advance for any inconsistencies that may arise as I've researched and developed each section.

1.1 Advanced Introduction to Enthalpy (Energy) Changes in Chemical Reactions

1.1a I have ASSUMED you have studied the GCSE notes on the basics of chemical energy changes

in what you might call a lower level introduction which bridges GCSE and AS level and you are completely ok in interpreting enthalpy level and activation energy diagrams such as ...

... and can clearly distinguish between enthalpy change and activation energy and the activation energy change with a catalyst does NOT change the enthalpy value of the reaction (activation energy will be rarely mentioned until the end of Part 3), but all important ideas from the GCSE page will be re-studied in their advanced level context, but I would still study the GCSE page first!

REMEMBER - all chemical changes are accompanied by energy changes or energy transfers, many of which can be directly measured, or, theoretically calculated from known values.

1.1b Enthalpy Changes and Thermochemistry

Some important initial definitions and examples:

The system: The reactants and products of the reaction being studied i.e. the contents of the calorimeter.

The surroundings: The means the rest of the 'world' including the i.e. a copper calorimeter, the surrounding air etc. etc.

Enthalpy H: The heat energy content of a substance. This cannot be determined absolutely but enthalpy changes for a chemical reaction can be measured directly or indirectly from theoretical calculations using known enthalpy values.

Enthalpy change ΔH: The net heat energy transferred to a system from the surroundings or from the surroundings to a system at constant pressure. The Greek letter delta Δ in maths implies a change, in this case a net heat energy change.

ΔH = H_final - H_initial  (the units of delta H are kJ mol^-1)

or ΔH = ∑H_products - ∑H_reactants

or ΔH^θ(reaction) = ∑ΔH^θ_f(products) - ∑ΔH^θ_f(reactants)

The Greek letter delta Δ implies 'change in' ....

The Greek letter ∑ implies 'sum of' ....'

ΔH^θ_f denotes a standard enthalpy of formation - which is explained further down.

Exothermic reaction

A reaction in which heat energy is given out from the system to the surroundings i.e. the enthalpy of the reacting system decreases and the temperature of the system and surroundings rises.

This means H_reactants > H_products so that ΔH is negative (-ve).

The enthalpy of the reaction system is decreasing.

Example: All combustion reactions are exothermic

e.g. CH_4(g) + 2O_2(g) ==> CO_2(g) + 2H₂O_(l)  ΔH = -890 kJmol^-1

i.e. the figure of 890 kJ released refers to the complete combustion of 1 mole of gaseous methane (24 dm³), using exactly 2 moles of gaseous oxygen (48 dm³) to form exactly 1 mole of gaseous carbon dioxide (24 dm³) and 2 moles of liquid  water. These values refer to 298K (25^oC and 1 atm/101 kPa)

Note some general points (which apply to all exothermic or endothermic changes, physical or chemical changes):

(i) All enthalpy values must be quoted with referenced to the ambient/assumed temperature and pressure of the system undergoing the physical or chemical change.

The usual standard reference conditions are 298K (25^oC and 1 atm/101 kPa), and other criteria may apply e.g. 1 molar solution if applicable.

(ii) Not only the molar quantities must clearly indicated BUT the physical states of all the substances must be clearly stated too.

This is a convenient point to make the point about the importance of state symbols via the combustion of hydrogen. eg

H_2(g) + ¹/₂O_2(g) ==> H₂O_(l)  ΔH = -285.9 kJ mol^-1, but for

H_2(g) + ¹/₂O_2(g) ==> H₂O_(g)  ΔH = -241.8 kJ mol^-1

If the water forms remains as steam/vapour/gas, then 44.1 kJ less heat energy is released to the surroundings, because condensation is an exothermic process (g ==> l) and forming liquid water releases an extra 44.1 kJ. The -285.9 (~-286) kJ mol^-1 is the usual value for the enthalpy of combustion of hydrogen you will encounter in your studies because at the standard temperature of 298K water is a liquid in its normal stable state.

(iii) This sort of combustion reaction can be measured in a calorimeter (see section 1.3). BUT, however the enthalpy change is measured, all equations should be read in molar terms when dealing with enthalpy values i.e. a delta H value goes with a specific equation.

(iv) Enthalpy change values are usually quoted in kJ mol^-1, but take care in their interpretation because you must know what equation goes with the ΔH value!

eg the enthalpy of combustion usually refers to the complete combustion of one mole of the combustible material as for water above, BUT if you double the equation you must also double the enthalpy values for that equation

2H_2(g) + O_2(g) ==> 2H₂O_(l)  ΔH = 2 x -285.9 =  571.8 kJ mol^-1

 

Endothermic reaction

A reaction in which the system takes in or absorbs heat energy from the surroundings i.e. the enthalpy of the system increases and the temperature of the system and surroundings falls OR the system must be heated to initiate the reaction and provide the heat absorbed.

This means H_products > H_reactants so that ΔH is positive (+ve).

The enthalpy of the reaction system is increasing.

Example: The thermal decomposition of calcium carbonate

CaCO_3(s) ==> CaO_(s) + CO_2(g)  ΔH = +179 kJmol^-1

i.e. 179 kJ of heat energy must be absorbed to decompose 1 mole of solid calcium carbonate into 1 mole of solid calcium oxide and 1 mole of gaseous carbon dioxide. M_r(CaCO₃) = 100, so 17.9 kJ of heat energy is absorbed in decomposing 10g of limestone. This reaction requires an experimental temperature of 800-1000^oC to achieve an appreciable rate of reaction and cannot be studied quantitatively in the laboratory. However it can be theoretically calculated from known enthalpy change values by means of a Hess's Law cycle calculation.

The two diagrams below illustrate how exothermic (left) and endothermic (right) reactions are specified on an enthalpy level diagram.

Standard conditions

Standard conditions for referencing enthalpy values are essential for communicating accurate data throughout the scientific community.

It means values measured/calculated in one laboratory/research team can be used in another scientific establishment anywhere!, OR checked for accuracy by any other scientists.

In this way accurate enthalpy data can be built up and through time validated and perhaps more accurately measured with technological developments and theoretical calculations become more reliable.

This means the reactants/products start/finish at a specified temperature, pressure and concentration whatever the 'temporary' temperature change in the reaction - which is required to calculate the enthalpy change.

The net energy change is based on the products returning to the same temperature and pressure that the reactants started at. The most frequently used standard conditions are a temperature of 298 K/25^oC (K = 273 + ^oC) and a pressure of 1 atm/101 kPa and a concentration of 1.00 mol dm^-3.

The use of standard conditions enables a database of delta H change to be assembled from which you can do theoretical calculations (see section 1.2 using Hess's Law).

Strictly speaking the standard conditions should be indicated in terms of the standard temperature and the reactants involved and standard delta H values are denoted with the Greek letter theta (θ).

By using data based on standard. agreed and defined conditions, then the data can be used universally by any laboratory around the world and also allows scientists to check each others experimental results.

Its pertinent here to consider the question - how can you have an standard enthalpy of combustion at 25^oC when the flame temperature is perhaps peaking at over 1000^oC !!!

The answer applies to all enthalpy changes what-so-ever!

The enthalpy change represents the heat energy change needed to restore the products to the temperature of the reactants at the start e.g. room temperature/25^oC.

Standard Enthalpy of Reaction ΔH_{r/react/reaction} is the enthalpy change (heat absorbed/released, endothermic/exothermic) when molar quantities of reactants as stated in an equation react under standard conditions (i.e. 298K/25^oC, 1 atm/101kPa)

Examples

(i) NaOH_(aq) + HCl_(aq) ==> NaCl_(aq) + H₂O_(aq)  (exothermic)

ΔH^θ_r,298 = -57.1 kJ mol^-1 (can also be described as an 'enthalpy of neutralisation')

(ii) CaCO_3(s) ==> CaO_(s) + CO_2(g)  (endothermic)

ΔH^θ_r,298 = +179 kJ mol^-1 (can also be described as an 'enthalpy of thermal decomposition')

Standard Enthalpy of Formation ΔH_{f/form/formation} is the enthalpy change when 1 mole of compound is formed from its constituent elements with both the compound and elements in their standard states ('normal stable states) i.e. at 298K/25^oC, 1 atm/101kPa

(a) It may be endothermic or exothermic

(b) Any accompanying equation should involve the formation of 1 mole of the compound

The standard state is the most stable state at the standard temperature and pressure e.g. at 298K/25^oC and 1 atm/101kPa

e.g.  H_2(g)  H₂O_(l)  C_(s)  O_2(g), C₃H_8(g)  C₈H_18(l)  C₂₄H_50(s)  CO_2(g)  CH₃CH₂OH_(l)  etc.

Examples

(i) C_(s) + 2H_2(g) ==> CH_4(g)   ΔH^θ_f,298(methane) = -74.9 kJ mol^-1

(ii) 2C_(s) + 2H_2(g) ==> C₂H_4(g)   ΔH^θ_f,298(ethene) = +52.3 kJ mol^-1

(iii) 2C_(s) + 3H_2(g) + ¹/₂O_2(g) ==> CH₃CH₂OH_(l)   ΔH^θ_f,298(ethanol) = -278 kJ mol^-1

(iv) ¹/₂N_2(g) + O_2(g) ==> NO_2(g)   ΔH^θ_f,298(nitrogen dioxide) = +33.9 kJ mol^-1

Note (a) The values can be positive/endothermic or negative/exothermic.

(b) The enthalpy of formation of elements in their standard stable states is arbitrarily assigned a value of zero.

This definition, together with experimental values of enthalpy changes allows a body of enthalpy change data to be accumulated and extended via theoretical calculations.

Standard Enthalpy of Combustion ΔH_{c/comb/combustion} is the enthalpy change when 1 mole of a fuel (or any combustible material) is completely burned in oxygen (or air containing oxygen) equated to standard conditions (298K/25^oC, 1 atm/101kPa).

You should ensure just 1 mole of fuel appears in the equation to accompany the delta H value which is always negative i.e. always exothermic.

Examples

(i) C₃H_8(g) + 5O_2(g) ==> 3CO_2(g) + 4H₂O_(l)  ΔH^θ_c,298K(propane) = -2219 kJ mol^-1

(ii) CH₃COOH_(l) + 2O_2(g) ==> 2CO_2(g) + 2H₂O_(l)  ΔH^θ_c,298K(ethanoic acid) = -876 kJ mol^-1

In the calculations explained below just the subscripted letters r/f/c will be used for brevity and a temperature of 298K and a constant pressure 1atm assumed unless otherwise stated. There is more the enthalpies of combustion of alkanes and alcohols in section 1.4a

Standard enthalpy of neutralisation is the energy released when unit molar quantities of acids and alkalis completely neutralise each other at 298K (pressure effects are insignificant for reactions only involving liquids/solutions/solids)

(i) NaOH_(aq) + HCl_(aq) ==> NaCl_(aq) + H₂O_(l)  ΔH^θ_{neutralisation} = -57.1 kJ mol^-1

(ii) Ba(OH)_2(aq) + 2HNO_3(aq) ==> Ba(NO₃)_2(aq) + 2H₂O_(l)  ΔH^θ_{neutralisation} = -116.4 kJ mol^-1

(iii) ¹/₂Ba(OH)_2(aq) + HNO_3(aq) ==> ¹/₂Ba(NO₃)_2(aq) + H₂O_(l)  ΔH^θ_{neutralisation} = -58.2 kJ mol^-1

Note! It looks as if the enthalpy of neutralisation of barium hydroxide is approximately double that of sodium hydroxide ie ~ twice as exothermic! Well yes it is! and no it isn't!

Yes - ~twice as much energy is released per mole of soluble base/alkali.

No - however, on the basis of heat released per mole of water formed, they are actually very similar.

In other words, which value you quote, depends on which point you want to make.

Yet another example of carefully qualifying enthalpy values with respect to the context.

More on enthalpies of neutralisation

Bond Enthalpy ('bond energy')

This is the average energy absorbed to break 1 mole of a specified bond when all species involved are in the gaseous state.

e.g. for (i) H_2(g) ==> 2H_(g)  ΔH = +436 kJ mol^-1  for the H-H bond

or for (ii) CH₃CH₂Br_(g) ==> CH₃CH_2(g) + Br_(g)  ΔH = +276 kJ mol^-1  for the C-Br bond

It is always endothermic and the reverse process - bond formation, is always exothermic. In many cases the values are averaged from a variety of 'molecular' situations. More on this in the bond enthalpy section.

Some examples of points made on this page with reference to an enthalpy level change diagram

General points: Arrows pointing downwards represent exothermic changes and arrows pointing upwards represent endothermic changes

1. The energy released when 1 mole of aluminium oxide is formed.

The ΔH value of -1669 kJ mol^-1 corresponds to the very exothermic enthalpy of formation of Al₂O₃ or the enthalpy of the complete combustion of two moles of Al.

The very exothermicity of the reaction suggests, and correctly, that aluminium oxide is a very stable compound - it is thermally stable to at least 2500^oC.

2. The endothermic enthalpy of formation of gold(III) oxide

It is a compound not readily formed and it decomposes on heating at ~150^oC, so contrast this thermal instability with that of aluminium oxide.

3. This is a much more complex enthalpy level diagram involving hydrogen, chlorine and hydrogen chloride.

The +436 kJmol^-1 represents the bond enthalpy for splitting hydrogen molecules into hydrogen atoms.

The +242 kJmol^-1 is the bond energy of chlorine molecules.

The -184 kJmol^-1 is the enthalpy of formation of hydrogen chloride gas.

The very exothermic -862 kJmol^-1 is the energy released theoretically when two moles of hydrogen chloride are formed directly from hydrogen and chlorine atoms.

The latter indicates that the H-Cl bond enthalpy is +862/2 = 431 kJmol^-1

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